Robust model for discrete competitive facility location problem with the uncertainty of customer behaviors

Two customer behavior rules that commonly employed in the literature of competitive facility location problem are the binary rule and the proportional rule. Most of the research is based on the assumption that customers patronize facilities in accordance with one of the two customer behavior rules or their variants. But a basic problem behind this assumption is: can it be confirmed that all customers follow one of the behavior rules? Actually, the heterogeneity of customer behaviors is more common than homogeneity, at the same time, the uncertainty within customer behaviors may lead to worse results for the original optimal solutions. This is the motivation to study competitive facility location problem with customer behavior uncertainty. In this paper, a robust model for competitive facility location problem is presented at first, which is established to deal with the uncertainty within two customer behaviors. A sort-based algorithm for solving the inner sub-problem of the robust model is designed by proving its optimal solution form. Then the improved ranking-based algorithm is proposed to solve the robust model. Finally, a quasi-real case and some benchmark problems are used to demonstrate the effectiveness and efficiency of the model and algorithm.